Jarzynski Equality — Nonequilibrium Work

Protocol Parameters

Protocol speed (τ steps) 10 steps (fast)

Temperature (β⁻¹ = k_BT) kT = 1.00

ΔF (true free energy gap) ΔF = 1.50

Trajectories per batch 100

Results

N trajectories0

⟨W⟩ (mean work)—

⟨e⁻βW⟩—

ΔF estimated—

True ΔF—

Dissipated work ⟨W_diss⟩—

The Jarzynski equality (1997) is an exact thermodynamic identity: the exponential average of work done in any nonequilibrium process equals the equilibrium free energy difference. This is remarkable — even irreversible, dissipative protocols work. The second law says ⟨W⟩ ≥ ΔF (Jensen's inequality), with equality only for quasi-static processes. Fast protocols produce broad work distributions, but rare low-W trajectories dominate the exponential average.